Higher order elliptic and parabolic systems with variably partially BMO coefficients in regular and irregular domains

Details Higher order elliptic and parabolic systems with variably partially BMO coefficients in regular and irregular domains Higher order elliptic and parabolic systems with variably partially BMO coefficients in regular and irregular domains

2011-02-08

arxiv.org/abs/1102.1489v1

Journal of Functional Analysis (2011), 261 (11), 3279-3327

Mathematics

Analysis of PDEs

45 pages, submitted in Nov. 2010

Scientific paper

10.1016/j.jfa.2011.08.001

The solvability in Sobolev spaces is proved for divergence form complex-valued higher order parabolic systems in the whole space, on a half space, and on a Reifenberg flat domain. The leading coefficients are assumed to be merely measurable in one spacial direction and have small mean oscillations in the orthogonal directions on each small cylinder. The directions in which the coefficients are only measurable vary depending on each cylinder. The corresponding elliptic problem is also considered.

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